The present invention relates to hybrid estimating filters and, in particular, to filters employing Kalman filtering techniques and digital and analog circuitry.
Observation of a process may be difficult because of noise of two types: the process itself may experience random disturbances. Secondly, the measurement itself may be subjected to noise that obscures the actual observation.
Well-known estimation methods include least squares estimation and maximum likelihood estimation. In Bayesian estimation, data on previous observations are used to refine an estimate. This technique tends to produce more accurate results but is more difficult to calculate. A stochastic process may be considered a Gauss-Markoff process if its future is independent of its past and its interfering noise is Gaussian.
Kalman filtering techniques employ the Bayesian techniques to provide estimates for a process that is assumed to be Gauss-Markoff. In a Gauss-Markoff process, the state of a process is equal to a process noise plus a prior state vector times a matrix transfer function. In this process, the measurement is obtained in the presence of an interference referred to as process noise.
In a discrete-time Kalman filter, a presumed probability density function is used as a basis for estimating the mean and covariance. As actual observations are obtained, the estimation equations are updated, based upon actual observations. In a continuous time case, the process is often assumed to be represented by a linear differential equation. A result of these assumptions is a filter which has a circuit that simulates the process under observation but has certain of its signals modified in accordance with the density function of the interfering noise.
The disadvantage of performing Kalman filtering digitally is the requirement of a powerful computer for providing real time estimates of the signal contained within a noisy measurement. This clearly increases the complexity and cost of such a filtering system.
A disadvantage with estimates obtained with analog filters is that the accuracy of the estimate is sacrificed in order to provide a real time output.
Staircase generators have been employed to produce sawtooth waves. In U.S. Pat. No. 4,620,291 a sawtooth waveform is generated through a digital to analog converter. Starting digitally, the waveform has many discrete jumps. The discrete signal is applied to a delay line having many taps. The taps are averaged together to provide a relatively smooth waveform. The system is not, however, used for providing a filtered output with Kalman techniques. Other circuitry for involving sawtooth and staircase generators are shown in U.S. Pat. Nos. 3,628,061; 3,676,784; 3,918,046; 3,919,649; and 4,144,579.
Accordingly, there is a need for a filter using estimation techniques that avoids the complexity of a digital Kalman filter without sacrificing.